We search for a light Higgs boson A0 in the radiative decay Upsilon(3S)-->gammaA(0), A(0)-->tau+tau-, tau+-->e+nu(e)nu(tau), or tau+-->mu+nu(mu)nu(tau). The data sample contains 122x10(6) Upsilon(3S) events recorded with the BABAR detector. We find no evidence for a narrow structure in the studied tau+tau- invariant mass region of 4.03<m(tau+tau-)<10.10 GeV/c2. We exclude at the 90% confidence level (C.L.) a low-mass Higgs boson decaying to tau+tau- with a product branching fraction B(Upsilon(3S)-->gammaA(0))xB(A(0)-->tau+tau-)>(1.5-16)x10(-5) across the m(tau+tau-) range. We also set a 90% C.L. upper limit on the tau+tau- decay of the eta(b) at B(eta(b)-->tau+tau-)<8%.